mlsanityData to 14 Oct 2026

Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series

arXiv 2202.07857 ↗First posted 16 Feb 2022cs.LG stat.MLcited by 42

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Abstract (arXiv)

Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time series, however, is a challenging subject, owing to the intricate interdependencies among the constituent series. We hypothesize that anomalies occur in low density regions of a distribution and explore the use of normalizing flows for unsupervised anomaly detection, because of their superior quality in density estimation. Moreover, we propose a novel flow model by imposing a Bayesian network among constituent series. A Bayesian network is a directed acyclic graph (DAG) that models causal relationships; it factorizes the joint probability of the series into the product of easy-to-evaluate conditional probabilities. We call such a graph-augmented normalizing flow approach GANF and propose joint estimation of the DAG with flow parameters. We conduct extensive experiments on real-world datasets and demonstrate the effectiveness of GANF for density estimation, anomaly detection, and identification of time series distribution drift.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). Builds on 28 of its 45 references that are in the map. First posted on arXiv 16 Feb 2022.

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28 of 45 references.

References · 28

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  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
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  5. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  6. 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,136
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  8. 2017Masked Autoregressive Flow for Density Estimationcited by 684
  9. 2020Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networkscited by 566
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16 more
  1. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  2. 2021Graph Neural Network-Based Anomaly Detection in Multivariate Time Seriescited by 301
  3. 2019Deep Semi-Supervised Anomaly Detectioncited by 291
  4. 2016Structured Sequence Modeling with Graph Convolutional Recurrent Networkscited by 275
  5. 2018Deep Anomaly Detection Using Geometric Transformationscited by 269
  6. 2016LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detectioncited by 215
  7. 2018Adversarially Learned One-Class Classifier for Novelty Detectioncited by 202
  8. 2017On the (Statistical) Detection of Adversarial Examplescited by 180
  9. 2021Discrete Graph Structure Learning for Forecasting Multiple Time Seriescited by 171
  10. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 144
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  12. 2018Object-centric Auto-encoders and Dummy Anomalies for Abnormal Event Detection in Videocited by 111
  13. 2019Graph Normalizing Flowscited by 104
  14. 2018Anomaly Detection with Generative Adversarial Networks for Multivariate Time Seriescited by 55
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 5; 2023: 13; 2024: 9; 2025: 5; 2026: 10.

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  1. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  2. 2022Deep Learning for Time Series Anomaly Detection: A Surveycited by 131
  3. 2023Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospectscited by 99
  4. 2024Large Language Model Guided Knowledge Distillation for Time Series Anomaly Detectioncited by 26
  5. 2023Navigating the Metric Maze: A Taxonomy of Evaluation Metrics for Anomaly Detection in Time Seriescited by 24
  6. 2022Detecting Multivariate Time Series Anomalies with Zero Known Labelcited by 21
  7. 2023Graph Anomaly Detection in Time Series: A Surveycited by 18
  8. 2023Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstructioncited by 17
  9. 2025Deep Learning Advancements in Anomaly Detection: A Comprehensive Surveycited by 17
  10. 2023Interpretation of Time-Series Deep Models: A Surveycited by 15
  11. 2023Explainable Time Series Anomaly Detection using Masked Latent Generative Modelingcited by 15
  12. 2024Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Seriescited by 15
30 more
  1. 2023Label-Free Multivariate Time Series Anomaly Detectioncited by 14
  2. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  3. 2024Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Valuescited by 10
  4. 2022Is it worth it? Comparing six deep and classical methods for unsupervised anomaly detection in time seriescited by 9
  5. 2022A Causal Approach to Detecting Multivariate Time-series Anomalies and Root Causescited by 8
  6. 2023The voraus-AD Dataset for Anomaly Detection in Robot Applicationscited by 7
  7. 2024PeFAD: A Parameter-Efficient Federated Framework for Time Series Anomaly Detectioncited by 7
  8. 2023GC-Flow: A Graph-Based Flow Network for Effective Clusteringcited by 5
  9. 2025DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Seriescited by 4
  10. 2023Contaminated Multivariate Time-Series Anomaly Detection with Spatio-Temporal Graph Conditional Diffusion Modelscited by 3
  11. 2024GDFlow: Anomaly Detection with NCDE-based Normalizing Flow for Advanced Driver Assistance Systemcited by 3
  12. 2024Interdependency Matters: Graph Alignment for Multivariate Time Series Anomaly Detectioncited by 3
  13. 2025ScatterAD: Temporal-Topological Scattering Mechanism for Time Series Anomaly Detectioncited by 2
  14. 2023OrionBench: Benchmarking Time Series Generative Models in the Service of the End-Usercited by 1
  15. 2024TreeMIL: A Multi-instance Learning Framework for Time Series Anomaly Detection with Inexact Supervisioncited by 1
  16. 2024FANFOLD: Graph Normalizing Flows-driven Asymmetric Network for Unsupervised Graph-Level Anomaly Detectioncited by 1
  17. 2025A Problem-Oriented Taxonomy of Evaluation Metrics for Time Series Anomaly Detectioncited by 1
  18. 2026Knowledge-Assisted Multi-Graph Dependency Learning for Multivariate Time Series Anomaly Detection in Multi-Stage Industrial Processescited by 1
  19. 2023Deep Generative Methods for Producing Forecast Trajectories in Power Systemscited by 0
  20. 2024Deep Multi-Manifold Transformation Based Multivariate Time Series Fault Detectioncited by 0
  21. 2025Causal Disentanglement Learning for Accurate Anomaly Detection in Multivariate Time Seriescited by 0
  22. 2026Anomaly Detection with Machine Learning Algorithms in Large-Scale Power Gridscited by 0
  23. 2026CGSTA: Cross-Scale Graph Contrast with Stability-Aware Alignment for Multivariate Time-Series Anomaly Detectioncited by 0
  24. 2026Temporal-Conditioned Normalizing Flows for Multivariate Time Series Anomaly Detectioncited by 0
  25. 2026GNNs for Time Series Anomaly Detection: An Open-Source Framework and a Critical Evaluationcited by 0
  26. 2026MO-SAE:Multi-Objective Stacked Autoencoders Optimization for Edge Anomaly Detectioncited by 0
  27. 2026Unified Taxonomy for Multivariate Time Series Anomaly Detection using Deep Learningcited by 0
  28. 2026VAN-AD: Visual Masked Autoencoder with Normalizing Flow For Time Series Anomaly Detectioncited by 0
  29. 2026Domain-Prior-Regularized Graph Modeling for Anomaly Detection in Cyber-Physical Systemscited by 0
  30. 2026RagGAD: Rationale-Aware Conditional Gaussian Mixture Normalizing Flow for Unsupervised Graph Anomaly Detectioncited by 0